Abstract
Stationary vortex sheets in a two-dimensional stirring flow may be approximated by arrays of stationary point vortices arranged along the support of the sheets. These vortices lie at the roots of a polynomial that satisfies a generalized Lame differential equation; the polynomial itself (not the roots) determines the complex potential and stream function. In this paper, sufficient conditions for the stirring flow are found so that the differential equation has two independent polynomial solutions with simple closed-form expressions, analogous to hypergeometric polynomials. The corresponding point vortex array then depends on a complex parameter that controls the location of the sheet, so that it may pass through any selected point. Stationary sheets in a periodic flow are approximated by the same method.
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